Least Action Principle and Energy Hamiltonian

The least action principle is an extremely powerful tool that can be used to determine the trajectories taken up by the particle. It simply states that out of the possible trajectories, the particle will take the one for which the action required is the least. The math involves forming a lagrangian and minimizing the overall lagrangian over the entire trajectory. We can think of it as jittering the trajectory slightly and finding the minimum action path in the neighbourhood. Since lagrangian has units of energy, we can think of it as a fancier version of energy minimisation. Owing to its generalised derivation, it is abundantly used in relativistic physics as well.

The concept could be further used to derive a generalised energy conservation principle. Do have a glance at these wonderful concepts!

Click here to read the quant side of it

Some useful external links:

1. Stanford

2. World Science Festival

3. Tensor calculus

4. Physics video by Eugene